Kreizhn
Nov16-10, 03:43 PM
Hey,
A quick question. In the definition of a differential form, we normally require that they be sections of the k-th exterior power of the cotangent bundle. However, on page 14 of Jurdjevic's book on Geometric Control Theory (http://books.google.ca/books?id=PpZXRUsBjgUC&printsec=frontcover&dq=geometric+control+theory&hl=en&ei=4vniTKyqLMSmngfwua2xDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCwQ6AEwAA#v=onepage&q=differential%20form&f=false), he defines them simply as sections of the cotangent projection.
Is there a mistake in his notes or does this represent an alternative way of examining differential forms?
A quick question. In the definition of a differential form, we normally require that they be sections of the k-th exterior power of the cotangent bundle. However, on page 14 of Jurdjevic's book on Geometric Control Theory (http://books.google.ca/books?id=PpZXRUsBjgUC&printsec=frontcover&dq=geometric+control+theory&hl=en&ei=4vniTKyqLMSmngfwua2xDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCwQ6AEwAA#v=onepage&q=differential%20form&f=false), he defines them simply as sections of the cotangent projection.
Is there a mistake in his notes or does this represent an alternative way of examining differential forms?